Multivariable Critical Points

[e^x]

The equations I got from setting the two partials equal to zero are:

y = 0.5 + 0.2x^2
x^2 = (4y + 4y^3)/5

When I try to solve for these I keep getting crazy decimals so I feel like I'm doing something wrong

 

[blamocur]

If you take the expression for [imath]x^2[/imath] from your second equation and plug it in into the first equation you get a cubic equation for [imath]y[/imath]. I don't know how you are expected to deal with cubic equations.

 

[BigBeachBanana]

 

[blamocur]

View attachment 29779
The equations I got from setting the two partials equal to zero are:

y = 0.5 + 0.2x^2
x^2 = (4y + 4y^3)/5

When I try to solve for these I keep getting crazy decimals so I feel like I'm doing something wrong

I don't know whether you are doing something wrong, but when I plotted the cubic polynome the root did not look pretty either.